represents a Gaussian white noise process with mean 0 and standard deviation 1.
represents a Gaussian white noise process with mean 0 and standard deviation σ.
represents a white noise process based on the distribution dist.
- WhiteNoiseProcess is also known as independent identically distributed (iid) process.
- WhiteNoiseProcess is a discrete-time random process.
- The slices of WhiteNoiseProcess are assumed to be independent and identically distributed random variables.
- The distribution dist can be any univariate distribution with mean 0 and finite variance.
- WhiteNoiseProcess can be used with such functions as Mean, PDF, Probability, and RandomFunction.
Examplesopen allclose all
Basic Examples (1)
Add white noise to a periodic signal:
Define a moving-average process:
Mean, variance, and kurtosis for the process:
Compare with the property values for the corresponding MAProcess:
Properties & Relations (6)
WhiteNoiseProcess is a discrete-time process:
The states may either be continuous or discrete:
SliceDistribution[WhiteNoiseProcess[dist],t] is equal to dist:
Multivariate slices are products of dist with itself:
The slice mean is always zero:
WhiteNoiseProcess is uncorrelated according to the AutocorrelationTest:
Gaussian white noise is a special case of an MAProcess:
Possible Issues (1)
EstimatedProcess fails for this example involving white noise from a uniform distribution:
Using a symmetric interval for UniformDistribution helps in this case:
Wolfram Research (2014), WhiteNoiseProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/WhiteNoiseProcess.html.
Wolfram Language. 2014. "WhiteNoiseProcess." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/WhiteNoiseProcess.html.
Wolfram Language. (2014). WhiteNoiseProcess. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WhiteNoiseProcess.html